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1 - Preliminaries

Published online by Cambridge University Press:  19 April 2019

Kai Liu
Kai Liu
Affiliation:
Tianjin Normal University, China
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Summary

In this chapter, we shall recall some definitions and results from functional analysis, partial differential equations, and probability theories. We introduce two notions of solutions, strong and mild, for stochastic differential equations in Hilbert spaces. We also introduce and clarify various definitions of stochastic stability in abstract spaces, which are a natural generalization of deterministic stability concepts.
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Chapter
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Stochastic Stability of Differential Equations in Abstract Spaces , pp. 1 - 45
Publisher: Cambridge University Press
Print publication year: 2019

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  • Preliminaries
  • Kai Liu, Tianjin Normal University, China
  • Book: Stochastic Stability of Differential Equations in Abstract Spaces
  • Online publication: 19 April 2019
  • Chapter DOI: https://doi.org/10.1017/9781108653039.002
Available formats
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  • Preliminaries
  • Kai Liu, Tianjin Normal University, China
  • Book: Stochastic Stability of Differential Equations in Abstract Spaces
  • Online publication: 19 April 2019
  • Chapter DOI: https://doi.org/10.1017/9781108653039.002
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Preliminaries
  • Kai Liu, Tianjin Normal University, China
  • Book: Stochastic Stability of Differential Equations in Abstract Spaces
  • Online publication: 19 April 2019
  • Chapter DOI: https://doi.org/10.1017/9781108653039.002
Available formats
×